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Spectrum of Light- and Heavy-Baryons

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Abstract

A symmetry-preserving truncation of the strong-interaction bound-state equations is used to calculate the spectrum of ground-state \(J=1/2^+\), \(3/2^+\) \((qq^\prime q^{\prime \prime })\)-baryons, where \(q, q^\prime , q^{\prime \prime } \in \{u,d,s,c,b\}\), their first positive-parity excitations and parity partners. Using two parameters, a description of the known spectrum of 39 such states is obtained, with a mean-absolute-relative-difference between calculation and experiment of 3.6(2.7)%. From this foundation, the framework is subsequently used to predict the masses of 90 states not yet seen empirically.

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Notes

  1. Given this “doublet” structure, \(64+64=128\) independent scalar functions are required to completely describe a nucleon Faddeev amplitude: see Appendix B in Ref. [61] for more details.

  2. In all calculations herein, we employ a mass-independent momentum-subtraction renormalisation scheme for all relevant DSEs, implemented by making use of the scalar Ward–Green–Takahashi identity and fixing all renormalisation constants in the chiral limit [75], with renormalisation scale \(\zeta =19\,\)GeV\(=:\zeta _{19}\).

  3. We reiterate that the mass-scale in Eq. (14) makes no allowance for the effect of corrections to RL truncation on light-hadron observables. This issue is canvassed elsewhere [81], with the following conclusion: for systems in which orbital angular momentum does not play a big role, the impact of such corrections may largely be absorbed in a redefinition of this scale. With some revisions, we adapt this idea below to systems with angular momentum and to radial excitations.

  4. The formulation of this problem and efficient solution methods are detailed, e.g. in Ref. [61], Appendices A–C, and Ref. [68], Appendices A, B.

  5. As it was above, in all subsequent cases the sensitivity to \(\pm 10\)% variations of \(\omega \) in Eq. (14), with \(D\omega =\,\)constant, is uniformly \(\lesssim 1\)%. We therefore omit further mention of it hereafter.

  6. Notably, the mass of any given hadron is an integrated (long-wavelength) quantity; hence, not very sensitive to details of the system’s wave function. This feature plays a big role in the success of the ESR: so long as the centre-of-mass for each excitation-level is correctly set by the symmetry-preserving treatment of a broadly-sensible interaction, then a fair description of the spectrum should follow. Dynamical quantities that evolve with a probe’s momentum scale, e.g. elastic and transition form factors, are needed to expose a bound-state’s internal structure and so reveal details of the interaction which forms the composite system.

  7. Given current experimental data on the splittings between parity partners and radial excitations in systems with heavier quarks, one cannot be certain whether the interaction strength should be changed in s, c, b channels. Theoretically, on the other hand, if these observed splittings are driven by DCSB, as we believe, then the effects should diminish with increasing current-quark mass. In that case, within the accuracy of our approach, it is sensible to modify only the light-quark interaction strength.

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Acknowledgements

We are grateful for constructive comments and encouragement from L. Chang, C. Chen, Z.-F. Cui, R. Gothe, V. Mokeev, J. Segovia, S.-S. Xu and P.-L. Yin; and for the hospitality of RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany. Work supported by: National Natural Science Foundation of China (NSFC) under Grant Nos. 11805024 and 11847301. Fundamental Research Funds for the Central Universities (China) under Grant No. 2019CDJDWL0005; Jiangsu Province Hundred Talents Plan for Professionals; U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357; and Forschungszentrum Jülich GmbH.

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Authors and Affiliations

  1. Department of Physics, Chongqing University, Chongqing, 401331, People’s Republic of China

    S.-X. Qin

  2. Argonne National Laboratory, Lemont, IL, 60439, USA

    C. D. Roberts

  3. Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425, Jülich, Germany

    S. M. Schmidt

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  1. S.-X. Qin
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  2. C. D. Roberts
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  3. S. M. Schmidt
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Correspondence to C. D. Roberts.

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Qin, SX., Roberts, C.D. & Schmidt, S.M. Spectrum of Light- and Heavy-Baryons. Few-Body Syst 60, 26 (2019). https://doi.org/10.1007/s00601-019-1488-x

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